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%I #8 Jan 04 2024 07:25:14
%S 4,12,16,18,20,24,27,28,36,44,48,50,52,54,60,64,68,72,76,80,84,90,92,
%T 98,100,108,112,116,120,124,126,132,135,140,144,148,150,156,160,162,
%U 164,168,172,176,180,188,189,192,196,198,204,208,212,216,220,228,234,236,240,242,244
%N Numbers that are not coprime to the maximal exponent in their prime factorization.
%C Subsequence of A137257 and first differs from it at n = 51.
%C Numbers k such that gcd(k, A051903(k)) > 1.
%C Includes all the nonsquarefree terms of A336064.
%C The asymptotic density of this sequence is 1 - 1/zeta(2) - Sum_{k>=2} (1/(f(k+1, k) * zeta(k+1)) - 1/(f(k, k) * zeta(k))) = 0.24998449199080279703..., where f(e, m) = Product_{primes p|m} ((1-1/p^e)/(1-1/p)).
%H Amiram Eldar, <a href="/A368715/b368715.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[210], !CoprimeQ[#, Max[FactorInteger[#][[;;, 2]]]] &]
%o (PARI) lista(kmax) = for(k = 2, kmax, if(gcd(k, vecmax(factor(k)[,2])) > 1, print1(k, ", ")));
%Y Cf. A051903.
%Y Subsequence of A013929 and A137257.
%Y Similar sequences: A060476, A074661, A096432, A336064, A368714.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, Jan 04 2024